The benchmark data sets are taken from a variety of sources around the world.
These sources include industrial collaborators and scientific publications. Most of the instances
are based on real world scenarios and a lot of them are nurse rostering problems.

All problem instances and best known solutions can also be found under /Benchmarks in the
installation directory of RosterViewer.

These instances are based on the data used by Greet Vanden-Berghe
in her PhD thesis "An Advanced Model and Novel Meta-heuristic Solution Methods to Personnel
Scheduling in Healthcare" [VAN02] and in the papers
[BUR99] and [BUR01].
A formal description of her model is also available here.

BCV-2.46.1

Best Solutions

Date

Found by

1572

Lower Bounds

Date

Found by

1572

The only employees able to receive D shifts are A, B and C and A, B and C cannot work any shift type other than D.
Using this decomposition, the optimal assignment of D shifts to these employees has a combined penalty of 612.
Looking at all the other employees and examining the constraints for cover, complete weekends and personal requests
only, it is possible to show that there is an unavoidable penalty of 960. Therefore a total unavoidable penalty of 1572.

BCV-3.46.2

Best Solutions

Date

Found by

894

Lower Bounds

Date

Found by

894

Linear programming formulation solved using column generation.

BCV-4.13.1

Best Solutions

Date

Found by

10

Lower Bounds

Date

Found by

10

Only employee A can be assigned DH shifts without a penalty being incurred. However there are 29 DH shifts to assign and
A can work a maximum of 19 without incurring a penalty which is larger than if they were assigned to other employees.
Therefore the other 10 DH shifts must be assigned to other employees at the expense of an unavoidable penalty of 10.

10

Linear programming formulation solved using column generation.

BCV-5.4.1

Best Solutions

Date

Found by

48

Lower Bounds

Date

Found by

48

This very small instance can be solved to optimality using CPLEX.

BCV-7.10.1

Best Solutions

Date

Found by

381

Lower Bounds

Date

Found by

381

Looking at the cover constraints, there are 1184 hours of work to assign. There are also
5 annual leave requests which counts as 30 hours of work. However, looking at the max hours worked constraint, the employees
request a max total of 1026 hours of work. Therefore in order to satisfy cover, (1184 + 30) - 1026 = 188 hours of overtime
will have to be assigned. This creates an unavoidable penalty of 376 (weight=2). Using this IP model
we can also show using CPLEX that there is
an unavoidable penalty of 5 in the week in which the annual leave requests are made. This gives a lower bound for the full
problem of 381.

BCV-8.13.1

Best Solutions

Date

Found by

148

Lower Bounds

Date

Found by

148

Employee A can only work DH shifts and no other employees can work the DH shifts. Hence in order to satisfy cover,
A has an unavoidable penalty of 20. Looking at the cover constraints, there are 1600 hours of work to assign.
There are also 20 annual leave requests which counts as 160 hours of work. However, looking at the max hours worked constraint, the employees
request a max total of 1632 hours of work. Therefore in order to satisfy cover, (1600 + 160) - 1632 = 128 hours of overtime
will have to be assigned. This creates an unavoidable penalty of 128. Therefore there is a total unavoidable penalty of 148.

These instances were provided by Gerhard Post.
A description of the problem is available here.

GPost

Best Solutions

Date

Found by

5

Lower Bounds

Date

Found by

5

28-Aug-2008

CPLEX solving a relaxed model.
The relaxation assumes one shift type and removes all constraints except:
Cover, one shift per day, no split weekends, min and max shifts per week,
max consecutive working weekends, on-off-on and off-on-off sequences, shift requests
and consecutive working days.

5

Apr-2009

Linear programming formulation solved using column generation.

GPost-B

Best Solutions

Date

Found by

3

07-Oct-2008

Enumerating all feasible schedules (work patterns)
with score <= 2 (there are 16679 for full timers and 65298 for part timers) and then using CPLEX to assign them.
It takes CPLEX 10 about 8 seconds to solve it (on a Core 2 Duo 2.83GHz). The OPL project is
available here.

Lower Bounds

Date

Found by

3

07-Oct-2008

Solved to optimality using CPLEX by enumerating
all feasible schedules (work patterns) with score <= 2.

These instances are the ones described in Ikegami and Niwa's 2003
paper [IKE03]. They are also available at Ikegami's homepage.
They were originally solved by Ikegami and Niwa using a hybrid tabu search.

These data sets are physician and nurse rostering problems
from hospitals in the area of Montreal, Canada. Most of the data sets are relatively large
(up to 6 weeks planning horizon and 50+ employees). In these instances,
cover requirements are
specified by time period of the day rather than per shift type.
The data was provided by Gilles Pesant.

This is an instance taken from a fairly early nurse rostering paper by Musa and
Saxena [MUS84]. The solution given in their paper with objective function value 199 required
28.3 seconds using a UNIVAC 1100. The optimal solution is 175 (solved using this IP model).

This is the January instance in [BUR05]
and instance 12 in [BUR07] by Burke et al.
To model the problem with minimal changes, some of the hard
constraints in the original problem have been changed to soft constraints
but with very large weights. Feasible solutions (i.e. solutions without the highly weighted
soft constraints broken) are known to exist though.

ORTEC01

Best Solutions

Date

Found by

270

02-Aug-2008

DeWolf Fan Xue using a hybrid variable depth search.

Lower Bounds

Date

Found by

270

13-Aug-2008

CPLEX solving a relaxed model. The relaxation models the
first five days only, assumes one shift type and removes all constraints except:
Cover, one shift per day, no split weekends, min and max shifts per week,
and min and max consecutive working days.

This data is based on a problem from Queen's Medical Centre University Hospital
NHS Trust, Nottingham, UK. The problem was originally examined by Petrovic and Beddoe
[BED04, BED06, PET03]
who used case-based reasoning to solve it.
In 2006, the problem was re-examined by Landa Silva and Le, who used a
multi-objective evolutionary approach.
The instances provided here are based on the problem formulation used by
Landa Silva and Le
(which is also very similar to the original problem).
In instance QMC-1, the only changes from
Landa Silva and Le's model are: the hard constraints have been changed
to soft constraints but with a weight of 1000 and the coverage constraint is a hard
constraint.
Instance QMC-2 is a alternative formulation which is closer to the original
formulation and in which over and under cover is allowed but penalised
(that is, part of the objective function).

This instance was taken from [VAL00] by Valouxis and Housos.
It is problem number 1 in their paper.
In the formulation here the hard constraints all have weight 1000 or higher.
As described in the paper,
the soft constraints are related to the lengths of feasible shift stretches. That is,
stretches of length two have weight x, stretches of length three have weight y etc.
The actual weights used by the authors are not mentioned in the paper but I am
trying to contact the authors to find out out the weights used for the results given in their paper.
The solution given in their paper has three workstretches of length two and two of length three. The current best
solution given on this website has one workstretch of length three.

Valouxis

Best Solutions

Date

Found by

20

Lower Bounds

Date

Found by

20

06-Oct-2008

CPLEX solving a relaxed model.
The relaxation merges all the shifts into one type. All feasible schedules with
score <= 40 are then generated. The problem is then to select 16 of these
schedules in order to satify cover whilst minimising the total score. The OPL project
is available here.

This instance was presented by Weil et al. in [WEI95].
The hard constraints have a weight of 1000 or higher. The constraints they describe as soft, have weights of 1.

WHPP

Best Solutions

Date

Found by

5

Lower Bounds

Date

Found by

5

02-Sep-2008

In order to satisfy cover,
90 D shifts, 110 E shifts and 70 N shifts must be assigned. This equals exactly 2100 hours.
Each employee requests max 70 hours work and there are 30 employees. Therefore each employee
has to receive exactly 70 hours in order to satisfy cover. N shifts are 10 hours
and D and E shifts are 7 hours each. An employee cannot work N and D or E shifts and
achieve exactly 70 hours work (there are no combinations of shifts which equal 70 hours other than
7 N's or 10 D's and E's). The problem can then be decomposed into assigning N's to 10 employees
and E's and D's to the other 20 employees. Solving a relaxed model of the latter problem
using CPLEX provides a lower bound of 5.

Beddoe, G.R. and S. Petrovic,
Selecting and Weighting Features Using a Genetic Algorithm in a Case-Based Reasoning Approach to Personnel Rostering.
European Journal of Operational Research, 2006. 175(2): pp. 649-671.

Tellier, P. and G. White. Generating Personnel Schedules in an Industrial Setting Using a Tabu Search Algorithm,
in Proceedings of the 6th International Conference on the Practice and Theory of Automated Timetabling.
2006. Brno, Czech Republic. pp. 293-302.